This replaces the earlier Insulae, and has practically the same effect. However, you'll need an additional District in each city in order to use it. This shouldn't be a problem for older cities, as each of them should have at least 3 districts already.
The logic of using Medina Quarter is the same - it is a great way to speed up Population growth in big cities which have already exhausted other Housing options, but have no access to Neighborhoods. However, you should juggle it with other 'permanent use' Economic Policies, such as Triangular Trade. .
Civilopedia Entry Edit
All Arab cities with some history left have their medina – an urban residential quarter typically walled, with narrow and maze-like streets, in some places less than a meter (39 inches) wide. To a follower of Islam, the Prophet decreed that a just and ordered city was obligatory, and so the design of medinas reflected communal values, often containing at their heart fountains, mosques, and markets. Because of their winding, narrow streets, they also served as defense against invaders… and they are also free of auto traffic, and usually of motorbikes, and even bicycles as well.